# Learning locally dominant force balances in active particle systems

arXiv: https://arxiv.org/abs/2307.14970 · HTML: https://mlsanity.com/paper/2307.14970/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 62 references that are in the map.
- First posted on arXiv 27 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks](https://mlsanity.com/paper/2107.00940/) (2021)
- [Learning normal form autoencoders for data-driven discovery of universal,parameter-dependent governing equations](https://mlsanity.com/paper/2106.05102/) (2021)
- [OpenFPM: A scalable open framework for particle and particle-mesh codes on parallel computers](https://mlsanity.com/paper/1804.07598/) (2018)
- [Learning deterministic hydrodynamic equations from stochastic active particle dynamics](https://mlsanity.com/paper/2201.08623/) (2022)

## Abstract (arXiv)

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate, and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, like asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.